ultimate seismic bearing capacity of strip · pdf file(friction circle method) with radius of...

129 AbdelAziz Ahmed Ali Senoon, Ultimate Seismic Bearing Capacity Of Strip Footing Using Modified

Krey’s Methods (Friction Circle Method), pp. 129 - 148

* Corresponding author.

E- Mail address:[email protected]

ULTIMATE SEISMIC BEARING CAPACITY OF STRIP

FOOTING USING MODIFIED KREY’S METHODS (FRICTION CIRCLE METHOD)

AbdelAziz Ahmed Ali Senoon

Civil Eng. Dept., Faculty of Eng., Assiut University, Assiut , Egypt.

Received 16 December 2013; accepted 29 February 2013

ABSTRACT

In geotechnical investigation, determination oftheseismic bearing capacity of foundation soil

constitutes an important task. The bearing capacity of soil under static loading has been extensively

studied since the early work of Prandtl (1921).Design of foundation in seismic areas needs special

considerations compared to the static case. The inadequate performance of structure during recent

earthquake has motivated researches to revise existing methods and to develop new method for

seismic resistant design. For foundation of structure built in seismic areas the demands to sustain load

and deformation during earthquake will probably be the severe in their design life. Due to seismic

loading foundation may experience decreases in bearing capacity and increases in settlement. Two

source of loading must be taken into consideration inertial loading caused by lateral forces imposed on

the superstructure, kinematic loading caused by the ground movement developed during earthquake.

Many techniques used for studying the effect of seismic forces on the soil bearing capacity such as, limit

equilibrium method, kinematic approach of yield theory, a variational approach, and unified theory of

stress, which the shape of failure surface has been assumed. The seismic forces are considered as pseudo-

static forces acting both on the footing and on the soil under the footing. However, finite element and

stress characteristics methods shape of the failure is not required to be assumed.

In the present paper, a theoretical analysis has been performed on the basis of Krey's method

(friction circle method) with radius of friction circle equal to = where r is the

radius of the circle slip surface to determine the influence of the earthquake acceleration coefficients

on the seismic bearing capacity of foundation with assisted by a computer program. The present

study is compared with the various theoretical solutions. The comparison of that the present study

predicted values of ultimate seismic bearing capacity of soil are less than others theories of ultimate

seismic bearing capacity. In order facilitate the calculation of seismic bearing capacity, using the

proposed equations. It is a function of (B, Rf, and c)

Keywords:Seismic Ultimate bearing capacity, strip footing, mechanism of failure, Centre location of

slip failure, shape of slip failure, Krey’s method

1. Introduction

In geotechnical investigation, determination oftheseismic bearing capacity of foundation

soil constitutes an important task. The bearing capacity of soil under static loading has

been extensively studies since the early work of Prandtl[17]. Design of foundation in

seismic areas needs special considerations compared to the static case. The inadequate

performance of structure during recent earthquake has motivated researches to revise

existing methods and to develop new method for seismic resistant design. For foundation

130

AbdelAziz Ahmed Ali Senoon, Ultimate Seismic Bearing Capacity Of Strip Footing Using Modified


Journal of Engineering Sciences, Assiut University, Faculty of Engineering, Vol. 42, No. 1, January,

2014, E-mail address: [email protected]

of structure built in seismic areas the demands to sustain load and deformation during

earthquake will probably be the severe in their design life.

Due to seismic loading foundation may experience decreases in bearing capacity and

increases in settlement. Two source of loading must be taken into consideration inertial

loading caused by lateral forces imposed on the superstructure and kinematic loading

caused by the ground movement developed during earthquake.

Many researchers have studied the seismic bearing capacity of shallow foundations [1-

24].The analytical solutions consist of limit equilibrium method as [3, 7, 8, 18, 19, 21],

kinematic approach of yield design theory [20], a variational approach [11, 22], unified

strength theory [4], stress characteristics [13], and finite element method

[12].DeepankarandSubba[8]used the limit equilibrium method for obtaining the seismic

bearing capacity factors of footing considering a composite failure surface with new

methodology.Vesic et al [22]have been used a pseudo–static method base on a variational

approach for evaluating the seismic bearing capacity of strip footing. In this method, the

inertia force is treated as an equivalent concentrated force (pseudo-static force) applied at

the center gravity of the structure.Castelli and Motto [10]used Bishop's of slices method

with a limit equilibrium method which the failure slip surface as circular from foundation

propagates until the ground surface is reached. Chen et al [4] utilized pseudo-static

analysis and taking the effect of intermediate stress into consideration based on the unified

strength theory. He concluded that the reduction of bearing capacity is mainly due to the

inclination effects resulting from cyclic earthquake shear and normal loads because of

structural inertia. The ratio of seismic to static bearing capacity factors depend on the

accelerations coefficients of seismic. Roberto and Pecker [20] used the kinematic approach

of yield design theory for evaluating the seismic effects on the ultimate bearing capacity of

shallow foundation on Mohr- Coulomb soil. The development of a new kinematic

mechanism taking into account the possible uplift of the foundation under strong load

eccentricities has permitted the investigation of the general case where the foundation is

subjected to combined action of inclined and eccentric load as well as soli inertia. Kumar

and Mohon[13] used the method of stress characteristics for determining the ultimate

seismic bearing capacity factors.In this method, the shape of the failure surface is not

required to be assumed, which the solution is obtained by satisfying simultaneously the

equilibrium and failure conditions everywhere within the plastic domain.

Many experimental work have been done to determine the seismic ultimate bearing

capacity and mechanism of failure for soil under footing [1, 5, 16, 23, 24]

With the latest advances in computer speed, linear and nonlinear analyses have found

more applications in soil mechanics including the seismic bearing capacity problem have

been used. However, finite element solutions are approximations to the exact solution.

Finite element method used to determine seismicultimate bearing capacity of soil [12].

They have been used the finite element method with pseudo-static approach to estimate the

seismic bearing capacity of strip footing which satisfies Mohr-coulomb strength criterion

for wide range of and seismic coefficient using Plaxis 2D. They concluded that soil

inertia plays a negligible role compared to the structural seismic load.





In the present work, a numerical study is carried out for the strip footing to investigate

the effect of the footing width and depth to width ratio rest on the humongous soil (c,φ ) on the ultimate seismic bearing capacity using modified Krey’s method[14] assisted by a computer , MATLAB, program,

2. Modified Krey’sMethod for Seismic Analysis

In fact, the surface failure of the soil due to footing load is continuous surface not

broken lines. Krey (1936) suggested a graphical method to determine the soil bearing

capacity under strip footing. The surface being assumed to consist of a circular arc

underthe footing, terminating in a tangent at (Choudhury and SubbaRao[7]

degrees to the ground. Krey’s method is the same friction circle method of the stability

of slop. The radius of the friction circle equal to .Krey statedthat

the center of the most dangerous circle would lieon the same level as the underside of the

footing andvarious trial centers are taken at this level.

Krey’smodels contain active zone ABDJK and passive zone DGJ. Failure occurs when

passive zone sliding up on the plane DG by the effect of rotating mass of the active zone

about center of arc BD see Fig.(1).

Fig. 1. Failure mechanism, according to Krey’s method (after [5])

132





Fig.2. Determine seismic ultimate bearing capacity force (Qultd) using modified

Krey’s method (friction circle method)

2.1.The graphical procedure is as follows

1- Let the centre of the slip surface on the same level as the underside of the footing

(Fig. (2).

2- Measure DJ and calculate E for JDG to get

Ppe=0.5 *kpe (DJ) 2 + 2xcxDJx√

Where [ √ ] (Egyptian code)(202/6)

where ( )

For determining the resulting position of the seismic passive earth pressures do the

following:

Determine the static passive earth pressure by using kps

Determine the seismic passive earth pressure by using kpe

The seismic force equal Pps-Ppe

The position of the resultant of reduction due to seismic at h above the point D

3- Measure the area ABDJK and calculate W= area(ABDJK)*

4- The resultant of the horizontal force E = Ppe –W(1-kh)

5- Determine the resultant E and W to give R1

6- Determine the cohesive force along the slip surface

S=c*Larc = c*r* α

with distance from centre of slip ⁄

7- Find the resultant of W, E and S to give R





8- Now there are three forces at only one point R (resultant of (W, E and S), F (soil

resultant reaction on slip surface, known direction and application point tangent of

friction circle from left side but undetermined value) and Qultd(ultimate load can

carry by footing, know direction and application point.

9- Draw a tangent to the friction circle through M (intersected R, Qultd) to obtain the

direction of the F, the force triangle can be completed and Qultdcan be obtained.

10- This procedure is repeated for several trial circles and the minimum value of

theQultdcan be obtained.

To avoid the phenomenon of shear fluidization (i.e., the plastic flow of the material at

finite effective for the certain combination of kh and kv (Richards et al (1990) and

from the stability criteria (Sarma (1990) the consider in the analysis are to

satisfy the relationship given by

In the present study all trials which were and shown in Fig.2 produced automatically by

the program and Qultd (seismic ultimate bearing load) can be easily obtained.

3. Main Aim of the Present Work

The main aim of the present work is to transfer the shown case of the seismic bearing

capacity of soil, using the modified Krey’s method into group of equations can be solved easily by computer with accuracy. Many trials are used to find the minimum soil seismic

bearing capacity which center of the slip arc locates on line pass on base of footing.

4. Parameters Used In the Program

4.1. Footing characteristics

Footing width B= 1, 2, 3 and 4 m

Ratio of footing depth to footing width, (Rf = 0.0, 0.5, 1, 1.5 and 2

4.2. Soil properties

Cohesion of soil c = 0, 2, 4, 6 and8 t/m2

Angle of internal friction of soil φ = 5, 10, 15, β0, β5, γ0, γ5, 40 and 45 degree.

4.3. Ground accelerations coefficient

Kh = 0.0, 0.2, 0.4 and 0.6 and kv=0.0

5. Procedure of Calculations

1. For a constant value of B=1(width of footing) and kh = 0.0 henceφ is changed nine

time φ = 5, 10, 15, β0, β5, γ0, γ5, 40 and 45 and corresponding Qultd(seismic

ultimate load) was obtained. Theultimate seismic bearing capacity can be

determined by (Qultd/B), maximum extent of failure surface, w, where

134





= ( ) =

( )

, and maximum depth of failure surface ,

2. The value B is changed four times = 1, 2, 3 and 4and step No. 1 is repeated.

3. The value khis changed four times = 0.0, 0.2, 0.4 and 0.6 and step No. 1 and 2 is

repeated.

4. For Rf (Depth to width ratio) =0, 0.5, 1.0, 1.50 and 2 steps 1,2 and 3 are repeated.

5. For c= 0, 2, 4, 6, and 10 t/m2steps 1, 2, 3 and 4 are repeated.

6. Results for steps 1, 2, 3, 4 and 5 are shown in figures (3-10)

7.

Fig. 3.Ultimate seismic bearing capacity versus at Rf = 0.0, kh =0.2 for

different values of B

1

10

100

1000

0 0.2 0.4 0.6 0.8 1

Se

ism

ic u

ltim

ate

be

ari

ng

ca

pa

city

(t/m

2)

tan (Φ)

B = 1.0 m

B = 2.0 m

B = 3.0 m

B = 4. m





Fig. 4.Ultimate seismic bearing capacity versus at Rf = 0.0 for different

values ofkh

Fig. 5. Ultimate seismic bearing capacity versus at Rf = 1.5 for different

values ofkh

1

10

100

1000

0 0.2 0.4 0.6 0.8 1

Se

ism

ic u

ltim

ate

be

ari

ng

ca

pa

city

(t/m

2)

tan (Φ)

Kh = 0.0

Kh = 0.2

kh = 0.4

kh = 0.6

2

20

200

0 0.2 0.4 0.6 0.8 1

Se

ism

ic u

ltim

ate

be

ari

ng

ca

pa

city

(t/m

2)

tan (Φ)

kh = 0.0

kh = 0.2

kh = 0.4

kh = 0.6

136





Fig.6.Ultimate seismic bearing capacity versus at Rf = 0, kh = 0.0 for

different values of c

Fig.7.Ultimate seismic bearing capacity versus at Rf = 0.0kh = 0.40 for

differentvalues of t c

1

10

100

1000

0 0.2 0.4 0.6 0.8 1

Se

ism

ic u

ltim

ate

be

ari

ng

ca

pa

city

(t/m

2)

tan (Φ)

c = 0.0

c = 2 t/m2

c = 4 t/m2

c = 6 t/m2

c = 8 t/m2

0.1

1

10

100

1000

0 0.2 0.4 0.6 0.8 1

Se

ism

ic u

ltim

ate

be

ari

ng

ca

pa

city

(t/m

2)

tan (Φ)

c = 0.0

c = 2 t/m2

c = 4 t/m2

c = 6 t/m2

c = 8 t/m2





Fig. 8. Maximum extent of failure surface (w/B) versus tan (φ) atRf = 0.5 c = 0.0

for differentvalues of kh

Fig. 9. Maximum depth of failure surface form ground surface (do/B) versus tan

(φ) at Rf = 0.5 c = 0.0 for different values ofkh

0

2

4

6

8

10

12

0 0.2 0.4 0.6 0.8 1

w/B

tan (Φ)

kh =0.0

kh= 0.2

kh = 0.4

kh =0.6

0

0.5

1

1.5

2

2.5

3

3.5

0 0.2 0.4 0.6 0.8 1

do

/B

kh = 0.0

kh = 0.2

kh = 0.4

kh = 0.6

138





Fig. 10. Maximum extent of failure surface (w/B) versus tan (φ) at Rf = 0.0 for

different values of c and kh

Fig. 11.Maximum depth of failure surface form ground surface (do/B) versus tan

(φ) at Rf = 0.5 for different khand c

6. Analysis and Discussion

The discussion illustrates the effect of foundation width, depth to width ratio, accelerations

seismic coefficients (khand kv) and soil properties (c,φ) on the following items:

Ultimate seismicbearing capacity of soil,qultd,

0

2

4

6

8

10

12

14

0 0.2 0.4 0.6 0.8 1

w/B

tan (Φ)

kh =0.0, c =0.0

kh = 0.2, c = 0 t/m2

kh = 0.2 , c= 2 t/m2

kh = 0.2 ,c =4 t/m2

kh = 0.2 ,c =8 t/m2

kh = 0.2, c = 20 t/m2

0.5

1

1.5

2

2.5

3

3.5

4

0 0.2 0.4 0.6 0.8 1

do

/B

tan (Φ)

kh = 0.0, c = 0.0

kh = 0.2, c = 0.0

kh = 0.2, c = 2 t/m2

kh = 0.2, c = 4 t/m2

kh = 0.2, c = 8 t/m2

kh = 0.2, c = 20 t/m2





Maximum extent of failure surface (w/B),

Maximum depth of failure surface (do/B) and

The deduced formula for determining qultd,,N q,Ncd,rc, rq and r

6.1. Seismic ultimate bearing capacity of soil (qultd)

The relation between ultimate seismic bearing capacity of soil(qultd) versustanφ (φ is the

angle of internal friction of soil) at different acceleration seismic coefficients (khand kv)are

plotted and shown in Figs. (3-7). It is clear that with increasing φ and B the qultdincreases

for a constant value of Rf. Figs.(3-4) have the same trend for the given values of Rf = 0.0 ,

0.5, 1,and 2). Figs (5-6) show the relation between qultdand tan (φ) for different value of

cohesion of soil, c.It is clear that with increasing φ and c the qultdincreasers for a constant

value of Rf. Figs.(5-6) have the same trend for the given values of Rf = 0.0 , 0.5, 1, 1.5 and

2. The ultimate seismic bearing capacity decreases considerably with increasing

accelerations coefficients.

6.2.Maximum extent of failure surface (w/B)

The relation between (w/B) versustan(φ) are plotted and shown in Figs. (8and 10). It is

clear that with increasing (φ) the w/B value increases.Fig (10) shows the relation between

(w/B) and tan (φ) for different,kh,andc. It is clear that by increasing (c)the (w/B) value

slightly effectfor a constant value of kh. Form Figs (9, 10) may be neglected the effect of

the cohesion of soil on the (w/B) and take the effect of friction only and accelerations

coefficients.

6.3.Maximum depth of failure surface from the ground surface (do/B)

The relation between ((do/B)) versustan (φ)are plotted in Figs. (9 and 11).It is clear that

with increasing φ the (do/B) increases and decreasing with kh. Fig (11) shows slightly

effect of c on the do/B while do/B decreases with increasing of kh.

6.4.The deduced formula for determining qultd,Nqd,Nγdand Ncd

6.4.1.Coshionless Soil c=0.0

Based on the results, the relation between qultdandtan φ is drawn for different values of B= 1, 2, 3 and 4, kh = 0.0, 0.2, 0.4, and 0.6 and Rf =0.0, 0.5, 1, 1.5 and 2. As shown in

Figs.(3-4) for Rf =0.0 and 0.5. At all cases the ultimate seismic bearing pressure increases

exponentially with increasing and linearly with increasing B at a certain Rf. The

relationship between qultdand B for the different values of φ, kh and Rf, may be represented

by the following expression

where a, b are coefficients obtained by regression formula depend on Rf, khand listed in

Table NO.1

140





0.1

1

10

100

1000

0 0.2 0.4 0.6 0.8 1

Nγd

tan(Φ)

kh = 0.0

kh = 0.2

kh = 0.4

kh = 0.6

Table 1.

a and b coefficients and deduced formula

Rf coefficients Horizontal accelerations coefficients Deduced formula

kh

0.0 0.2 0.4 0.6

0.0 a 0.572 0.154 0.120 0.117 0.170-0.092kh

b 6.390 6.347 5.861 4.648 7.317-4.247kh

0.5 a 0.880 0.403 0.316 0.348 0.410-0.136kh

b 5.632 5.039 4.344 3.594 5.77-3.612kh

1 a 1.09 0 0.728 0.715 0.847 0.644+0.297kh

b 5.572 4.706 3.858 3.133 5.472-3.932kh

1.5 a 1.180 0.917 1.186 1.592 0.556+1.687kh

b 5.750 4.684 3.595 2.815 5.5670-4.672kh

2 a 1.200 0.673 0.944 1.164 0.436+1.227kh

b 5.846 5.222 4.017 3.337 6.07- 4.707kh

Fig. 12. Seismic bearing capacity factor N d versus tan (φ) at different kh

6.4.2.Bearing capacity factor

The ultimate seismicbearing capacity of footing at the ground surface forcohesionless

soil can be expressed by the following equation

Where is the bearing capacity factor depend on angle of internal friction of soil, and

kh ,as shown in Fig. 12, may be represented by the following equation =





Where c, d are coefficient obtained by regression formula depend on khand are listed in

Table No. 2

Table 2.

c and d coefficients

kh 0.0 0.2 0.4 0.6 Deduced formula kh

Coefficient c 0.632 0.172 0.158 0.130 0.1953-0.105kh

Coefficient d 6.40 6.35 5.26 4.65 7.126-4.26kh

6.4.3.Bearing capacity factor

Based on the results, the relation between and is drawn for different values

of kh = 0.0, 0.2, 0.4, and 0.6 and Rf = 0.0, 0.5, 1, 1.5 and 2 as shown in Figs. (3-5). From

all cases the ultimate seismic bearing pressure increases exponentially with

increasing and linearly with increasing B at a certain Rf. The ultimate seismic bearing

capacity of soil can be divided into two parts. First part for surcharge load while second

part unit weight of soil. The relationship between qultdand B for the different values of kh, ϕ

and Rf, may be represented by the following expression

The value of versus tan (φ) is plotted for different values of kh as shown in Fig. 13. It

is clear that with increasing tan (φ) the value of increases and decreasing with

increases kh. The relationship between and tan (φ) may be represented by the following expression:

Where f, g are coefficients obtained by regression formula depend on khand listed in

Table No. 3

Table 3.

f and g coefficients kh 0.0 0.2 0.4 0.6 Deduced formula kh>0.0

Coefficient f 0.678 0.437 0.37 0.47

Coefficient g 4.96 4.41 4.23 2.736

142





Fig. 13. Seismic bearing capacity factor Nqd versus tan(φ) at different kh

6.4.4. Bearing capacity factor

Based on the results, the relation between and is drawn for different values

of c =0, 2, 4, 6 and 8t/m2,kh = 0.0, 0.2, 0.4, and 0.6 and Rf = 0.0, 0.5, 1, 1.5 and 2 as

shown in Figs.(6-7). From all cases the ultimate seismic bearing pressure increases

exponentially with increasing and linearly with increasing c at a certain kh. The

ultimate seismic bearing capacity of soil can be divided into three parts. First part for

cohesion, second part for surcharge loads while third part unit weight of soil for friction.

The relationship between qultdand B for the different values of c, φ and Rf, may be

represented by the following expression

The value of Ncd versus is plotted for different values Rf as shown in Fig.(7). It is

clear that with increasing the value of Ncd increases, and slightly decreases with

increasing Rf. the relationship between Nc and may be represented by the following

expression:-

Where h, z are coefficients obtained by regression formula depend on khand listed in

Table No. 3

1

10

100

0 0.2 0.4 0.6 0.8 1

Nq

d

tan (Φ)

kh = 0.0

kh = 0.2

kh = 0.4

kh = 0.6





Table 3.

h and z coefficients

kh 0.0 0.2 0.4 0.6 Deduced formula kh>0.0

Coefficient h 5.283 3.56 2.571 1.984

Coefficient z 2.858 2.455 2.173 1.95

Fig.14.Seismic bearing capacity factor (Ncd) versus tan φ at kh= 0.2for different Rf

Fig.15.Seismic bearing capacity factor (Ncd) versus tan φ for different kh

1

10

100

0 0.2 0.4 0.6 0.8 1

Ncd

tan (Φ)

kh = 0.0

kh = 0.2

kh = 0.4

kh = 0.6

0

5

10

15

20

25

30

35

40

45

0 0.2 0.4 0.6 0.8 1

Ncd

tan(Φ)

Rf = 0.0 Rf = 0.5

Rf = 1.0 Rf = 1.5

Rf = 2.0

144





7. Ratio of Seismic to Static Bearing Capacity Factors

The seismic to static bearing capacity factors depend on the acceleration ratio where

khand kv are the horizontal and vertical seismic coefficients with the failure zone. In

analysis subscripts d and s signify earthquake and static condition. A simple approach to

account for seismic effects is to reduce the static bearing capacity factors

where: , , .

The ratio of seismic to static bearing capacity factors are given in Table No. 4

Table 4.

Ratio of seismic to static factors and simple formula

Ratio kh Equation Average Simple formula

0.2 0.535 0.4 0.301

0.6 0.175 0.2 0.46 0.4 0.26

0.6 0.17 0.2 0.265 0.4 0.114

0.6 0.051

Form the Table No. 4 ratio of seismic to static bearing factors decreases with increasing

tan (φ) at a certain kh by small value, therefore taking the average value and use the simple

formula.All the deduced formula can be easily calculated by ordinary calculator.

8. Application of the Program and Deduced Formula and Comparison with

Others

Some examples were solved using program and the formulas given by author,

comparison with the references given in Figs (16-17). Fig. 16 shows the qultd versus tan (φ) at B =1 m, Rf = 1, c = 2t/m

2 and = 1.8t/mγusing different methods. It is clear that the

qultdby current method (modified Krey’s method) less than others methods. Fig.17 shows

the ratio between seismic to static bearing capacity factors from researches and current

method.





0

20

40

60

80

100

120

140

160

180

200

0 0.2 0.4 0.6 0.8 1

qu

ltd (

t/m

2)

tan(φ)

Ref.( 13 )

Ref.(12 )

fromula

Run program

Fig.16.Ultimate seismic bearing capacity versus at B = 1.0 m, Rf = 1, c = 2

t/m2

using different methods

Fig. 17 a. Bearing capacity factor (Ncd) versus tan φ using different methods

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.2 0.4 0.6 0.8 1

rc

tan(φ)

Ref. (12)

Ref.(19)

Ref.(3)

Ref.(4)

Run program

Simple formula

146





Fig.17 b. Bearing capacity factor (Nqd) versus tan φ using different methods

Fig.17 c. Bearing capacity factor (N d) versus tan φ using different methods

9. Conclusions

The horizontal acceleration, as soil properties (c, φ), effect on the seismic bearing

capacity coefficients significantly. The problem of the ultimate seismic bearing capacity

of strip footing using modified Krey’s method (friction circle method) on (c-φ ) soil can be easily analyses and solved to find the ultimate seismic bearing capacity , qultd,

bearing capacity factors (Ncd, Nqd and N d) , maximum extent of failure surface and

maximum depth of the failure from ground surface ((w/B) and (do/B)) by a simple

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 0.2 0.4 0.6 0.8 1

rq

tan(φ)

Ref. (12)

Ref.(19)

Ref.(3)

Ref.(13)

Run program

Simple formula

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.2 0.4 0.6 0.8 1

rϒ

tan(φ)

Ref. (12)

Ref. (19)

Ref. (3)

Ref.(13)

Ref. (20)

Run program

Simple fromula





program by author instead of a graphical methods used before in this method. The

recommend program based on footing characteristic and soil properties described in

details of the case study. Simple formulas were deduced base on results obtained from

run of computer program for the case study to calculate easily by a calculator (qultd, Ncd,

Nqd ,N d, rc, rq, and r ). A comparison was made between results of present work and

researches to evaluate to mention items. The obtained results approximately well agree

with some pervious work. In this provides the designer a means of evaluating the

seismic bearing capacity factors from the static ones.

10. References

[1] Awad A. Al-Karni& M. Budhu, (β001), “An experimental study of seismic bearing

capacity of shallow footings, “ Proceedings: Fourth International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamic and Symposium in

honor of Professor W.D. Laim Finn, San Diego, California, March 26-31.

[2] Bowles, J. E., "Foundation analysis and design," 5th Ed, Mc-Graw-Hill Int., Book Co., New

York, N.Y, (1996).

[3] Budhu,M. & AL-Karni, A. (199γ),” Seismic bearing capacity of soils,” Geotechnique 4γ, No. 1, 181-187.

[4] Chen Chang-fu., Dong Wu-zhongandand Tang Yan-zhe, (2007), “Seismic ultimate

bearing capacity of strip footings on slope, “ Journal Cent. South Univ. Technol. 05-

0730-07.

[5] D’Appolonia, D. J., D’Appolonia, E. D. and Brissette,R. F. (1968),” Settlement of spread

footings on sand,” J. SM &Fnds. Div., ASCE, 94, pp.1011-1053.

[6] Debasis Roy, (2013),"Design of shallow and deep foundations for earthquakes” Geotechnicalearthquake engineering IITGn- March 4-8, 1-8.

[7] Deepankar C. & K. S. SubbaRao (2005), “Seismic bearing capacity of shallow strip

footings,”Journal Manuf. Syst. 24(1), 117-127.

[8] Deepankar C. & K. S. SubbaRao (2006), “Seismic bearing capacity of shallow strip

footings embedded in slope.” International Journal of Geomechanics Vol. (6), No. 3, May.

Pp.176-184.

[9] Egyptian Code of Practice (ECP), (2002/6)"Soil mechanics, foundations design and

construction," Research Center for Housing, Building and Planning, Giza, Egypt.

[10] F. Castelli& E. Motta, (2013), “ Seismic bearing capacity of shallow foundations.” www.intechopen.com

[11] Garber M. and Baker R. , !997), “ Bearing capacity by variational method,” Journal of Geotechnical Engineering Division, Proceedings of the ASCE, Vol. 103, No. GT11, 1209-

1225.

[12] H. Shafiee, and M. Jahanandish, (2010), “Seismic bearing capacity factors for strip footings,” five National Congress on Civil Engineering, May 4-6, Ferdowsi University of

Mashhad, Mashhad, Iran.

[13] J. Kumar and V. B. K. MohonRao (β00β), “seismic bearing capacity factors for spread

foundations.”Getechnique 5β, No. β, 79-88.

[14] Krey, H. 19γ6) ERddruck, Erwiderstand” Earth Pressure Resistance and bearing of

soils” W. Ernst, Berlin pp. 14γ-146 .

[15] Meyerhof G. G. (195γ) “ The bearing capacity of foundation under eccentric and

inclined loads, Proceedings of the third International Conference in soil mechanics and

foundation engineering Vol. 1, 440-445.

http://www.intechopen.com/

148





[16] Okamoto, S. (1956),” Bearing capacity of sandy soil and lateral earth pressure during earthquake.” Proc. First World Conp. On Earthquake Eng. Berkeley, CA. Paper No.27.

[17] Prandtl, L. (19β1)” Uber die Eindringung-Sfestigkeit( Hart) PlasticherBaustoffe und die

Festigkeit Von Schneiden’ Zeitschrift Fur AnggewandlteMathematik und Mechanik Vol. 1 No.1 15-20 Basel, Switzerland **

[18] Richards, R., Elms,D. G., and Budhu, M. (1990),” Dynamic fluidization of soils” Journal

of Geotechnical Enghg Div., ASCE, Civil Engrs, 116, No. 5, 740-759.

[19] Richards, R., Elms,D. G., and Budhu, M. (1993), Seismic bearing capacity and

settlements of foundations, Journal of Geotechnical Engineering 119(4): 662-674

[20] Roberto Paolucci& Alain Pecker (1997), “Seismic bearing capacity of shallow strip

foundations on dry soils.” Soils and foundations, Vol.γ7, No. γ, 95-105, Japanese

geotechnical Society.

[21] Sarma S. K. and Iossifelis I.S., (1990), “Seismic bearing capacity factors of shallow strip footings.”Geotechnique 40 No. 2, 265-273.

[22] Soubra A. H. &Regenass, P. (1992)”Bearing capacity in seismic area by variational approach, Numerical models in Geomechanics, Pande&Pietruszczah (eds)Balkema

Rotterdam , ISBN 9054100885 PP.421-428.

[23] Vesic, A. S. Banks, D. C., and Woodard, J. M. (1965), “An experimental study of

dynamic bearing capacity of footing on sand.” Proceeding, 6th International Conference

on Soil Mechanics and Foundation Engineering, Montreal, Canada, 2, pp.209-213.

[24] Zeng, X. &Steedman, R.S. (1998), “Bearing capacity failure of shallow foundation in

earthquake,”Geotechnique, 48(2), 235-256.

دا طريقة كير المعدلة مية اسا شريطى باست ة تحمل سي اقصى ق) ا ائرة ااحت )طريقة

ص العربى المية تحديد اقصىى قىوت تح ىي مىي لية لة يبىة يم ىي لىل ااى ال اىاق ةيىح ال قىوت تح يىي ال ةيبىة فى اابحاث الجيوتق

( تصىى ي اامىىار فىىى ل قىىة 1291ال ةىىيت بيااىىدا اامىى اتيةية امىىاي اامىىار تىى توامىى ن ب ومىى لىىل اا ىىا ىىان الىى الا تفىى عىى ا ا اىى ة لحالىىة اامىى اتيةية ااتان ال يىىي ىىافى لة الىى الا يح ىىاى الىىى ا ىىاواا نابىىة بال

يق جديدت لة ص ي ال قا ق لة الا ةيح ال امامىاا ال ىااى ال ي ىة ال اةثيل الى لياجمة ال يق الجديدت ايجات ان ال الا ال ح ي ةد اا. ا جة لح ىي الى الا يحىدث اقىو لقىوت فى ل قة لالا تمااى لل ة ي تعةي ا . يوجد لصىدويل لحة ىا يجىن ال يانىى فىى اا ىاو الح ىي القصىووب ال اى ن تح ي ال يبة لياتت فى الا و

عىىل المةىىوب الح ىىي ا ىىان بوامىى ة القىىوب المياىىية ااتيىىة لىىل ال لةي يةىىى ال اىى ن بوامىى ة الحي ىىة ااواىىية ا ييقىة ااتى ال الحديىة يق تع خدق لدوامة تى يي قىوت الى الا ةىى قىوت تح ىي ال يبىة لثىي ال الا . توجد دت يق ت ةىن فىيش لىةي يية ااجاات ال وةد ةيح ال اى اج ال اااةى ا و ال يية الخ ي ةى ل اج الة ال

ابىي ال حىدتت م ح ااا ييقىة الم اياو قوت ال الا تانى بقوت اف يااية تؤ ي فى ال يبة اامىار لى الىيا ال يية الخصائو ا ت ةن فيش م ح ااااياولا قا. ا

يية ييب بمد تمديي اصى ق ىي تائىيت ااة ةىا لدوامىة تى يي يية بام خداق ا فى اىا ال قا اجييت توامة اال الالية ةى قوت ال ح ي الاي لية لة يبة ب اا دت بياىالج يىوتي ى تى لقاواىة الدوامىة الحاليىة لمالحا المجةة

ج فىى اىى الدوامىة ال قىوت ال ح ىي الاىي لية لة ةيبىة اقىي لىل الدوامىاا الاىابقة بالدواماا الاابقة ال اةىة امى ة ةىى ال ىائ ج ال ىى تى الحصىو ةياىا لىل ال ياىالج لم ىدت ةىى لااولة الحااباا ام خدلت لماتاا لق يةة ل ي

( φ ل اية ااة ةىا الىدانةى لة يبىة (Rf=Df/B( اا ة ق ال ميس الى يش اامار B يش اامار ( ةيح ي ةل ام خدالاا بوام ة الة الحام ة الماتية.kh( لمالي المجةة الاي لية c لمالي ت امك ال يبة

ultimate seismic bearing capacity of strip · pdf file(friction circle method) with radius of...

Documents